What is a good sequence through math for physicists?

[Thinker301]

Hello everybody, this is my first post.

I was wondering, what math a physicist needs. I know about the mathematical methods books, but I was hoping to learn as much math as I can rigorously. (I find it fascinating)

So what kind of course sequence would encompass a lot of the math needed for a physicists.

I have seen the guide for math on the string theory website, but a lot of it is very discrete. (Not class-type, rather one part of a class. (e.g. it separately lists lie groups, but I recently learned that you can learn that topic in an abstract algebra class))

Also what math books would accompany the course. (Highest rigor possible)

Here is the list I have accumulated so far :

High school Math (Basic Mathematics by Lang)
Calculus (Apostol)
Linear Algebra (Hoffman)
Differential Equations (Arnol'd)
Real Analysis (Pugh)
Complex Analysis (Polka or Rudin)
Abstract Algebra(Dummit and Foote or Artin)
Differential Geometry(Spivak)

I apologize if I am ignorant, I am just starting my journey. I am currently working on Apostol's Calculus(Vol. 1 at the moment).

 

[verty]

I think you may want to chart a more direct route.

Here is an interesting book: https://www.amazon.com/dp/0486658406/?tag=pfamazon01-20